There's actually a logical error here: if trading results were essentially random, a certain subset of traders (including day traders) would, at any given time, have profitable records. But you would not be able to derive (and, therefore, implement in code) any set of rules which would make automated trading profitable. You would just either be lucky, or not, as an algorithmic traders just as you would as any other kind of trader.
Now, I'm not saying that trading profits are random, but the existence of some profitable traders does not mean that there are rules you can deduce from their behavior that will guarantee profitable trading when implemented by someone else (either in an automated system or otherwise.)
It's relatively easy to have a profitable period on a strongly bull market. But it's irrelevant if any 'unexpected' (people call such events unexpected despite the fact that they tend to happen regularly over time) event such as 2008 crisis will completely wipe you out.
You're forgetting about the many that aren't profitable. You're also forgetting about the majority that are less profitable than the market average. The latter is probably the easiest to overlook. Yes, they are technically profitable, but so are packaged portfolios of stock held for long periods of time. If you can't be more profitable than someone who puts in zero effort, then whats the point of putting in more work?
Sure, it is possible to to program very niche behaviour, but we are nowhere near any sort of program that can act as general "day trader".
The stock markets are very far from a rational, perfect information game with simple rules.
Case in point is the fluctuations in Warren Buffett's fund whenever Anne Hathaway is in the news.
http://ftalphaville.ft.com//2011/03/28/528481/for-the-bots-a...
The best for you to start learning - would be to get a start on how the market works - my suggestion would be - https://www.amazon.com/dp/B000THOD1G/
A trader that is independent may still have advantages that prevent some random programmer from bootstrapping his/her way to also being an independent trader.
Just thinking out loud though, I'm not a trader of any sort.